Leonardo Torres Quevedo

Cableways

Torres' studies in the field of cableways began around 1880, during his residence in his hometown of Molledo. There, in 1885, he constructed the first cableway, which spanned a depression of some 40 metres (130 ft). The cableway was about 200 metres (660 ft) wide and carried a single person seated in a chair suspended from a cable, with another traction cable. The engine used to move the human cargo was a pair of cows. In 1887, he would build a much larger, motorized cableway over the Río León in Valle de Iguña [es], but it was intended solely for transporting materials.^[25][20]

These experiments formed the basis of his first patent application on 17 September, 1887, in Spain, "Un sistema de camino funicular aéreo de alambres múltiples" ("A multi-wire suspended aerial system"),^[26] for a passenger cableway system with which he achieved a level of safety suitable for transporting people, not just materials. The patent was extended to other countries: the United States, Austria, Germany, France, the United Kingdom, and Italy.^[27] His system introduced a multiple-cable support arrangement in which one end of a cable is anchored to fixed counterweights and the other (via a pulley system) to movable counterweights. With this system, the axial force of the cables is constant and equal to the weight of the counterweight, regardless of the load on the car. What varies with this load is the deflection of the cables, which increases as the counterweight is raised. Therefore, the safety factor of these cables is perfectly known and independent of the car's load. The resulting design is very robust and remains safe in case of a support cable failure.^[28][29]

In April 1889 Torres presented his cableway system in Switzerland,^[30] a place very interested in this means of transport due to its geography, between Pilatus-Kulm and Pilatus-Klimsenhorn (Mount Pilatus).^[31] It was an aerial funicular with a length of 2 km and a gradient of 300 m. In 1890 he traveled to that country to convince different authorities of its construction. He failed to convince the Swiss authorities, who did not grant any reliability to the work of a Spanish engineer due to contemporary skepticism surrounding early aerial transport systems.^[32] This disappointment, known as the "Swiss failure", led him to focus on other fields for several years.^[25] On 30 September 1907, Torres put into operation the first cableway of his system intended for safe public transport, the Mount Ulia aerial ropeway [es] in San Sebastián.^[33][34][35] The journey was 280 meters, with a drop of 28 meters, lasted for just over three minutes, and the gondola had the capacity to board up to 18 people on each trip. The execution of the project was the responsibility of the Bilbao Society of Engineering Studies and Works, founded in 1906 by Valentín Gorbeña to develop and commercialize Torres' patents.^[36] The Ulia cableway remained in operation until 1917 and the practical viability of its design paved the way for similar passenger transport systems in other countries.^[37]

The successful outcome of this type of aerial tramway gave him the opportunity to design the Spanish Aerocar based on J. Enoch Thompson's idea at Niagara Falls in Canada.^[38] The 550-meter-long system is a cableway that crosses the whirlpool in the Niagara Gorge on the Canadian side. It travels at about 7.2 kilometres per hour (4.5 mph). The load per cableway is 9 tonnes (9.9 short tons), with a safety factor for the cables of 4.6,^[39] and carries 35 standing passengers on a one-kilometer journey.^[40] It was built between 1914 and 1916. For its construction and assembly, the Niagara Spanish Aerocar Company Limited was created from the Society of Engineering Studies and Works, with a capital of $110,000 (roughly $3.5 million in 2025),^[41] and a planned 20-year concession. Construction was directed by Torres's son, Gonzalo Torres Polanco.^[42] It completed its first tests on February 15, 1916, and was officially inaugurated on August 8, opening to the public the following day. The system remains in operation with only minor modifications and has become a notable tourist and engineering landmark.^[43]

The Aero Car is considered the sole surviving example of Torres' design for an aerial ferry. Built and operated in Canada, it represents a fully Spanish-engineered project from conception to execution, designed by Torres and constructed by a Spanish company financed with Spanish capital. A plaque, mounted on a boulder in front of Aero Car Gift Shop recalls this fact: International Historic Civil Engineering Site. The Niagara Spanish Aerocar. A tribute to the distinguished Spanish Engineer who designed the Niagara Spanish Aerocar. This was only one of his many outstanding contributions to the engineering profession. Engineer Leonardo Torres Quevedo (1852–1936). Constructed 1914–1916. CSCE. The Canadian Society for Civil Engineering. 2010. Asociación de Ingenieros de Caminos, Canales y Puertos de España. Spanish aerial ferry of the Niagara.^[44]

Analog calculating machines

Algebraic machine

Endless spindle

Since the mid-19th century, several mechanical devices had been devised—including James and William Thomson's integrators, various multipliers, and Charles Babbage's never-completed analytical engine—setting the stage for Torres' own developments in the field. In 1893 he presented the "Memória sobre las máquinas algébricas" ("Memoir on Algebraic Machines") at the Spanish Royal Academy of Sciences in Madrid.^[45] This paper was commented on in a report by Eduardo Saavedra in 1894 and published in the Revista de Obras Públicas [es].^[46] Saavedra, who considered Torres' calculating machines as "an extraordinary event in the course of Spanish scientific production",^[47] recommended that the final project be financed.^[20]

In 1895 Torres presented "Sur les machines algébriques", accompanied by a demonstration model, at the Bordeaux Congress of the Association pour l'Avancement des Sciences.^[48] In 1900, he presented a comprehensive study, "Machines à calculer" ("Calculating machines") to the Paris Academy of Sciences. An abstract was published in its Comptes rendus that same year,^[49] followed by the full memoir in the Mémoires de l'Institut de France.^[50] The commission formed by Marcel Deprez, Henri Poincaré and Paul Appell, asked the academy for its publication, where they reported favorably: "In Mécanique analytique, Joseph-Louis Lagrange considers material systems whose connections are expressed by relationships between the coordinates or parameters used to define the position of the system. We can, and this is what Mr. Torres does, take the opposite point of view." Concluding: "In short, Mr. Torres has given a theoretical, general and complete solution to the problem of the construction of algebraic and transcendental relations by means of machines; moreover, he has effectively constructed machines that are easy to use for the solution of certain types of algebraic equations that are frequently encountered in applications."^[51][52]

His works examined the mathematical and physical analogies underlying analogical calculation or continuous quantities, and how to mechanically establish the relationships between them, expressed in mathematical formulas. The study included complex variables and used the logarithmic scale. From a practical standpoint, he demonstrated that mechanisms such as rotating discs could be used indefinitely with precision, so that changes in the variables were unlimited in both directions.^[53] Torres developed a whole series of analog mechanical calculating machines that used certain elements known as arithmophores,^[54] which consisted of a movable part and an index that allowed the quantity to be read according to its position.^[55] The aforementioned movable part was a graduated disc or drum that rotated on an axis. The angular movements were proportional to the logarithms of the magnitudes to be represented. Between 1910 and 1920, using several of these elements, Torres built an algebraic machine capable of calculating the roots of arbitrary polynomials of order eight, including complex ones, with an accuracy of up to thousandths.^[56] This machine could calculated the equation: ${\displaystyle \alpha ={\frac {A_{1}X^{a}+A_{2}X^{b}+A_{3}X^{c}+A_{4}X^{d}+A_{5}X^{e}}{A_{6}X^{f}+A_{7}X^{g}+A_{8}X^{h}}}\,}$ where X is the variable and A₁ ... A₈ is the coefficient of each term. Considering the case of α = 1, the following formula is obtained, and the root of the algebraic equation can be found: ${\displaystyle A_{1}X^{a}+A_{2}X^{b}+A_{3}X^{c}+A_{4}X^{d}+A_{5}X^{e}-A_{6}X^{f}-A_{7}X^{g}-A_{8}X^{h}=0\,}$

When calculating each term on a logarithmic scale, they can be calculated using only sums and products such as A₁ + a × log(X), which can handle a very wide range of values, and the relative error during the calculation is constant regardless of the size of the value. However, to calculate the sum of each term, it is necessary to accurately obtain log(u + v) from the calculated values log(u) and log(v) on a logarithmic scale. For this calculation, Torres invented a unique mechanism called the "endless spindle" ("fusee sans fin"), a complex differential gear that uses a helical gear shaped like a wine bottle, which allowed the mechanical expression of the relation ${\displaystyle y=\log(10^{x}+1)}$.^[57] Putting log(u) – log(v) = log(u/v) = V, then u/v = 10 V, and the following formula is used to calculate log(u + v): ${\displaystyle \log(u+v)=\log(v(u/v+1))=\log(v)+\log(u/v+1)=\log(v)+\log(10^{V}+1)\,}$,^[58][59] the same technique that is the basis of the modern electronic logarithmic number system.

Torres also devised another machine around 1900 with a small computing using gears and linkages to obtain the complex number solution of the quadratic equation X² – pX + q = 0, and an integrator to solve first-order differential equations.^[60] This mechanical phase later evolved into electromechanics, which he used to design and construct analytical machines.^[61] Nowadays, Torres' analog machines are kept in the Torres Quevedo Museum at the School of Civil Engineering of the Technical University of Madrid.^[62]

Aeronautics

In 1902, Torres started the project of a non-rigid, trilobed-shape dirigible designed to solve the serious problem of gondola suspension by including an interior framework of flexible cables that provided rigidity to the airship through internal pressure, a principle known as "autorigid".^[63] He applied for a patent in France entitled "Perfectionnements aux aerostats dirigibles" ("Improvements in dirigible aerostats"),^[64][65] wrote a "Note sur le calcul d'un ballon dirigeable a quille et suspentes interieures" ("Note on the calculus of a dirigible balloon with interior suspension and keel"), and presented both to Madrid and Paris' Academies of Science.^[66][67][68] By the end of that year the report at Paris's Academy of Science was included in the French magazine L'Aérophile,^[69] and an English-language summary was published in the British The Aeronautical Journal.^[70]

Torres was appointed director of the Centre for Aeronautical Research in Madrid in 1904, a civil institution created by the government of Spain "for the technical and experimental study of the air navigation problem and the management of remote engine maneuvers."^[71] From March 1905, with Army Engineer Captain Alfredo Kindelán as Technical Assistant, he supervised the construction of the first Spanish dirigible in the Army Military Aerostatics Service, located in Guadalajara, which was completed in June 1908. The new airship, named Torres Quevedo in his honor, made successful test flights with passengers in the gondola. However, Torres parted company with the Army and found himself forced to leave the Park in Guadalajara. Despite this, between 1907 and 1909 he had requested improved patents for his airship in the United Kingdom^[72] and France.^[73][74] He moved all the material to a rented hangar in Sartrouville (Paris), beginning a collaboration with the Société Astra, a new Aeronautical Society integrated in the conglomerate of French petroleum businessman Henri Deutsch de la Meurthe and directed by Édouard Surcouf, who had been familiar with Torres' work since 1901. The Astra company managed to buy the patent with a cession of rights extended to all countries except Spain, making the use of said system free in the country. In 1911, development began on dirigibles known as the Astra-Torres airships, and Torres would receive royalties of 3 francs for every m³ of each airship sold.^[68]

In 1910, Torres conceptualized a docking system to address the numerous difficulties engineers encountered when securing airships. His concept involved anchoring the craft's nose to a mooring mast, enabling the vehicle to pivot freely with changing wind directions. By tethering the bow to the top of a grounded metal tower via cable, dirigibles could be safely moored outdoors under any weather conditions. Moreover, the design envisioned enhanced infrastructure at temporary landing zones to facilitate passenger disembarkation. Patented in Belgium in February 1911— and subsequently in France^[75] and the United Kingdom^[76] in 1912—the system was officially titled "Improvements in Mooring Arrangements for Airships." Towers based on his design became standard industry practice, significantly improving aircraft accessibility and eliminating the labor-intensive process of manual hangar storage.^[77][78]

In February 1911, trials of the Astra-Torres No. 1 conducted at Issy-les-Moulineaux, south-west of Paris, proved successful. The airship, with a volume of 1,590 m³, reached speeds of up to 53 km/h.^[79] In May 1911, it won the Deperdussin Prize after recording the fastest time for a dirigible over a predetermined 100-kilometre circular course. Following this achievement, the airship participated alongside French military forces in the Bastille Day parade at Longchamp on 14 July 1911.^[80] Subsequent Astra-Torres designs included the Astra-Torres XIV (designated HMA No. 3 to the Royal Naval Air Service), which in September 1913 set a new world speed record for airships by reaching 83.2 km/h,^[81] and the Pilâtre de Rozier (Astra-Torres XV) named after the aerostier Jean-François Pilâtre de Rozier, which at 24,300 m3 was the same size of the German 'Zeppelins', reaching speeds of around 85 km/h.^[82]

The distinctive trilobed envelope was also employed in the United Kingdom in the Coastal, C Star, and North Sea airships.^[83] The Entente powers used these dirigibles during the First World War (1914–1918)^[84] for diverse tasks, principally to the escort of convoys, the continuous surveillance of coasts and the search, from bases in Marseille, Tunisia and Algeria, for German submarines in the Bay of Biscay, the English Channel and the Mediterranean Sea.^[85]

In 1919, based on a proposal by engineer Emilio Herrera Linares, Torres also designed a transatlantic dirigible named Hispania. The project aimed to achieve the first transatlantic flight for Spain, and was patented in both Spain^[86] and France,^[87] but was ultimately abandoned due to financial difficulties.^[88] The success of Torres' trilobed design during the war even drew the attention of the Imperial Japanese Navy in 1922, who acquired the Nieuport AT-2 with almost 263 ft long, maximum diameter 54 ft and with a hydrogen capacity of 363,950 ft 3.^[89] This type of non-rigid airship continued to be manufactured in various countries during the postwar era, notably by the French Zodiac Company in the 1930s, influencing the design of most later dirigibles.^[90]

Multi-command radio remote control

Telekino: transmitter.

Telekino: receiver.

Torres began developing remote control technology around 1901 or 1902, as a way of testing his airships without risking human lives. Between 1902 and 1903, he patented a radio control system in France,^[91] Spain,^[92] United States,^[93] and the United Kingdom,^[94] under the name "Systéme dit Télékine pour commander à distance un mouvement mécanique" ("Means or method for directing mechanical movements at or from a distance").

On 3 August 1903, Torres presented the Telekino (a term derived from two Greek words: tele (far away, in the distance) and kino (force, movement)) at the Paris Academy of Sciences, together with a detailed memoir,^[95] and making a practical demonstration to its members.^[96] He created a family of different and easily readable code words by using the signal generated with a common wireless telegraph transmitter, building a completely new type of receiver, which was able to react in a different way to each codeword sent by the transmitter.^[97] José Echegaray praised the Telekino as a material device capable of interpreting instructions "as if it were intelligent", referring to its operation as a form of "disciplined intelligence".^[98][99] For the construction of this first model, Torres received help from Gabriel Koenigs, the director of the Laboratory of Mechanics at the Sorbonne, and Octave Rochefort, who collaborated by providing wireless telegraphy equipment.^[100]

In 1904 Torres chose to conduct initial Telekino testings in the Beti Jai fronton of Madrid, which became the temporary headquarters of his Centre for Aeronautical Research until 1907,^[101] first in an electric three-wheeled land vehicle with an effective range of just 20 to 30 meters, which has been considered the first known example of a radio-controlled unmanned ground vehicle (UGV).^[96] In 1905, he tested a second model of the Telekino remotely controlling the maneuvers of an electric boat in the pond of the Casa de Campo in Madrid, achieving distances of up to about 250 m,^[102] and later testing a dinghy on the Bilbao Abra bay from the terrace of the Club Marítimo in the presence of the president of the Provincial Council and other authorities.^[103][104] The successful trials attracted significant international press attention.^[105]

On 25 September 1906, in the presence of the king Alfonso XIII and before a crowd, Torres successfully demonstrated the invention in the port of Bilbao, guiding the boat Vizcaya from the shore with people on board, demonstrating a standoff range of 2 km.^[106][107] By applying the Telekino to electrically powered vessels, he was able to select different positions for the steering engine and different velocities for the propelling engine independently. He was also able to act over other mechanisms such a light, for switching on or off, and a flag, for raising or dropping it, at the same time. Specifically, Torres was able to do up to 19 different pulse-coded actions with his prototypes. These experiences encouraged Torres to apply to the Spanish government for financial aid to use his Telekino for steering submarine torpedoes, a technological field that was just emerging. The government denied his application, leading him to abandon further improvements to the Telekino.^[108] Nevertheless, the Telekino laid the groundwork for Torres' research in automatics, anticipating many of his later theoretical and practical developments.^[109]

In January 1907, French inventor Gustave Gabet presented a wireless telemechanics device to the Paris Academy of Sciences based on a "delayed contact" principle. Torres formally contested Gabet's claims by submitting a note titled Le télékine et la télémécanique. Réclamation de priorité, which was received during the Academy's session on 4 March. In the text, Torres stated that this operating principle and its technical solutions were identical to those he had already patented for his Telekino in France in 1903. The Academy officially recognized his claim by publishing the note in the Comptes Rendus on 6 May.^[110]

Symbolic language for machine description

Torres introduced a formal language in Vienna in 1907 designed for the description of mechanical drawings and devices. He had previously published the concepts of this method in a paper titled "Sobre un sistema de notaciones y símbolos destinados a facilitar la descripción de las máquinas" ("System of notations and symbols intended to facilitate the description of machines") in the Revista de Obras Públicas.^[111] According to Austrian computer scientist Heinz Zemanek, this was equivalent to a programming language for the numerical control of machine tools.^[112]

Torres defined a table of symbols, established a set of rules, and applied them to a concrete example to demonstrate their technical viability. Through this symbolic language, he sought to address the limitations in contemporary mechanical description and design methods. Regarding the challenges of this endeavor, Torres noted:

"Charles Babbage and Franz Reuleaux—and I suppose others as well, although I have no record of them—have tried, without success, to remedy this drawback; but although these eminent authors have failed, that should not be a sufficient reason to abandon such an important endeavor."^[113]

Despite the independent efforts of Babbage, Reuleaux, and Torres, the engineering field continued to rely primarily on descriptive geometry as its standard symbolic language.^[114]

Laboratory of Automatics

As a member of the steering committee of the Board for Advanced Studies and Scientific Research [es] (Junta para la Ampliación de Estudios e Investigaciones Científicas (JAE))—established in Madrid in 1907 to promote scientific research and education in Spain^[115]—Torres played a leading role in creating three key state agencies. These agencies served as models for the JAE's multidisciplinary research support: the Laboratory of Automatics (1907), of which he was appointed director;^[116] the Association of Laboratories (1910), which unified state laboratories and workshops for instrument construction; and the Institute of Scientific Materials (1911), which managed budget allocations.

The Laboratory of Automatics produced a wide variety of instruments, building its own inventions while providing essential support and services to JAE universities and researchers. Torres, physicist Blas Cabrera, and workshop head Juan Costa jointly designed several scientific instruments, including a Weiss-type electromagnet, an X-ray spectrometer, a remote-control mechanism for a Bunge scale, and a variable-height reservoir with micrometer movements for magneto-chemical measurements. Additionally, prominent scientists commissioned custom equipment from the workshop: Ángel del Campo [es] —head of the Spectroscopy Section of the Laboratory of Physical Research and mentor to Miguel A. Catalán—ordered a spectrograph; Manuel Martínez Risco [es] requested a Michelson-type variable-distance interferometer; Juan Negrín acquired a stalagmometer; and Santiago Ramón y Cajal commissioned both a microtome and a panmicrotome, alongside a film projector.^[117][118]

The development of the Laboratory of Automatics reached its peak with the reform of the Palace of the Arts and Industry [es], to house the School of Industrial Engineers and the JAE, and the National Museum of Natural Sciences, also expanding the own laboratory.^[20] In 1939 the laboratory gave rise to the Torres Quevedo Institute of the Spanish National Research Council (Consejo Superior de Investigaciones Científicas, CSIC).^[119]

El Ajedrecista

"El Ajedrecista" No. 1 (The Chessplayer), complete view

"El Ajedrecista" No. 2, interior view

In 1910, Torres prepared the designs for a chess-playing device—which he dubbed El Ajedrecista (The Chess Player)—and in 1911 he began its construction in his laboratory.^[120] As opposed to The Turk and Ajeeb, El Ajedrecista was an electromechanical automaton capable of playing a king and rook endgame against a human opponent. Operating without any human intervention, the automaton achieved true integration of its mechanical and logical components from any starting position.^[121][122]

The pieces had a metallic mesh at their base, which closed an electric circuit that encoded their position in the board. When the black king was moved by hand, an algorithm calculated and performed the next best move for the white player.^[123] If an illegal move was made by the opposite player, the automaton would signal it by turning on a light. If the opposing player made three illegal moves, the automaton would stop playing.^[124] Due to the simplicity of its move-calculating algorithm, the automaton does not always deliver checkmate in the fewest moves possible, at times requiring more than the fifty moves permitted by the rules. However, it consistently defeated its opponents in every match.^[125] Claude Shannon, in his paper Programming a Computer for Playing Chess (1950), pointed out that Torres' idea was quite advanced for that period.^[126]

This FEN configuration and move sequence show how White executes Torres' algorithm to checkmate the black King:

[FEN "8/8/1k6/8/R7/8/5K2/8 w - - 0 1"]

1. Rh4 Kc5 2. Kf3 Kd5 3. Ke3 Kd6 4. Rh5 Kc6 5. Ke4 Kd6 6. Rg5 Kc6 7. Kd4 Kd6 8. Rg6+ Kd7 9. Kd5 Ke7 10. Rh6 Kf7 11. Ra6 Ke7 12. Rb6 Kf7 13. Ke5 Ke7 14. Rb7+ Kd8 15. Ke6 Kc8 16. Rh7 Kb8 17. Rg7 Ka8 18. Kd6 Kb8 19. Kc6 Ka8 20. Kb6 Kb8 21. Rg8#

Following its completion in 1912, the automaton was first demonstrated in 1913 at the Asociación Española para el Progreso de las Ciencias in Valladolid.^[127][128] It had its official public debut at the University of Paris in 1914, where it drew great interest and was featured on the front page of Le Matin.^[129] Its internal construction was published by Henri Vigneron in the French magazine La Nature.^[130][131] On 6 November 1915 Scientific American magazine in their Supplement 2079 pp. 296–298 published an illustrated article entitled "Torres and His Remarkable Automatic Devices. He Would Substitute Machinery for the Human Mind". It was summarized as follows:^{[132][133][134]}

"The inventor claims that the limits within which thought is really necessary need to be better defined, and that the automaton can do many things that are popularly classed with thought".^[134]

In November 1922, about to turn 70, Torres finished the construction designs of a second chess player, in which, under his direction, his son Gonzalo had introduced various improvements.^[135] The mechanical arms to move pieces were replaced for electromagnets located under the board, sliding the pieces from one square to another. This version included a phonograph record pronounced the words "echec et mat" when Black was checkmated.^[136][137] Torres initially presented it in Paris in 1923.^[127] Gonzalo later exposed the second chess player at several international meetings, introducing it to a wider audience at the 1951 Paris conference Les Machines à Calculer et la Pensée Humaine.^[138][139] The French National Centre for Scientific Research (CNRS) organized the conference, where Norbert Wiener attended and took on the machine in a match on January 12th or 13th.^[140][141] El Ajedrecista also defeated Savielly Tartakower at the conference, being the first Grandmaster to lose against a chess-playing machine.^[142][143]

In 1958, it was presented at the Brussels World's Fair, where Heinz Zemanek, who played with the device, described it as "a historical witness of automaton artistry that was far ahead of its time. Torres created a prefect algorithm with 6 subrules which he realized with the technological means of that time, essentially with levers, gearwheels, and relays."^[144] While it lacks the stored-program architecture of modern computers, El Ajedrecista has been considered the first computer game,^[145] having executed automated decision-making and chess computations that preceded later software-based chess programs by several decades.^[146]

Essays on Automatics

It has been commonly assumed (see Metropolis and Worlton 1980) that Charles Babbage's work on a mechanical digital program-controlled computer, which he started in 1835 and pursued off and on until his death in 1871, had been completely forgotten and was only belatedly recognized as a forerunner to the modern digital computer. Ludgate, Torres y Quevedo, and Bush give the lie to this belief, and all made fascinating contributions that deserve to be better known.

In January 1914, Torres published "Ensayos sobre Automática. Su definición. Extensión teórica de sus aplicaciones" (Essays on Automatics. Its Definition – Theoretical Extent of Its Applications) in the Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales [es].^[147] It was translated into French in 1915 with the title "Essais sur l'Automatique" in the Revue Générale des Sciences Pures et Appliquées.^[148]

Within this paper, Torres introduced what he called Automática (Automatics), a proposed new branch of the theory of machines devoted to the study of automata capable of regulating their actions according to changing circumstances. He explored "another type of automaton of great interest: those that imitate, not the simple gestures, but the thoughtful actions of a man, and which can sometimes replace him", thereby challenging Cartesian views on the inability of machines to imitate human reasoning. Torres distinguished between simpler automata, whose operation depended on fixed mechanical relationships, and a more advanced class whose relationships between operating parts could change "suddenly when necessary circumstances arise". Such automata would require sense organs, including "thermometers, magnetic compasses, dynamometers, manometers", together with mechanisms capable of carrying out the required operations and suitable power sources. He argued that the principal aim of Automatics was to endow machines with discernment, enabling them to take account of information received from their surroundings and adapt their behaviour accordingly. Such automata, he maintained, could make decisions provided that "the rules the automaton must follow are known precisely".^[149][150]

The paper provides the main link between Torres and Babbage. He gives a brief history of Babbage's efforts at constructing a mechanical Difference Engine and Analytical Engine. He described the Analytical Engine as exemplifying his theories as to the potential power of machines, and takes the problem of designing such an engine as a challenge to his skills as an inventor of electromechanical devices. It contains a complete design (albeit one that Torres regarded as theoretical rather than practical) for a machine capable of calculating completely automatically the value of the formula ${\displaystyle a^{x}(y-z)^{2}}$, for a sequence of sets of values of the variables involved. It demonstrates cunning electromechanical gadgets for storing decimal digits, for performing arithmetic operations using built-in function tables, and for comparing the values of two quantities. The whole machine was to be controlled from a read-only program (complete with provisions for conditional branching), represented by a pattern of conducting areas mounted around the surface of a rotating cylinder. The paper also contains an early description of a floating-point representation for numerical data, which historian Randell notes was described "almost casually".^[134] Torres proposed expressing numbers using a fixed number of significant digits together with a separate exponent indicating the order of magnitude, a practical convention intended to simplify mechanical computation by reducing the complexity required for numerical storage and processing. This representation is conceptually similar to modern floating-point notation.^[151] He did it in the following way:

"Very large numbers are as troublesome in mechanical calculations as in ordinary ones (Babbage planned 50 wheels to represent each variable, and even they would not be sufficient if we do not resort to the means that I will indicate later, or another analogous one). In the latter, the resulting inconveniences are ordinarily avoided by representing each quantity by a small number of significant figures (six or eight at most, except in exceptional cases) and indicating with a comma and with zeros, if necessary, the order of magnitude of the units represented by each figure.

Sometimes, to avoid writing many zeros, quantities are written in this form: ${\displaystyle n\times 10^{m}}$.

We could greatly simplify this notation by arbitrarily establishing three very simple rules:

1. n will always have the same number of digits (six, for example).

2. The first digit of n will be in the tenths place, the second in the hundredths place, and so on.

3. Each quantity will be written in this form: n; m.

Thus, instead of 2435.27 and 0.00000341682, we will write, respectively, 243527; 4 and 341862; −5.

I have not specified a limit to the value of the exponent; but it is evident that in all usual calculations it will be less than one hundred. Therefore, in this system, all the quantities involved in the calculations will be written using only eight digits."^[152]

The paper ends with a comparison of the advantages of mechanical devices that were all that were available to Babbage. Randell establishes that Torres would have been quite capable of building a general-purpose electromechanical computer more than 20 years ahead of its time, had the practical need, motivation, and financing been present.^[153]

Analytical machines

"The achievements of George Stibitz, Howard Aiken and IBM, and Konrad Zuse crown the transitional but crucial period of relays and their theorists. This stage on the path to automatic computing was built upon a concise and proven technology: that of electromagnetic relays. The modesty of this technological level serves to highlight the quality of the intellectual contributions of Torres y Quevedo, Alan Turing, and Claude Shannon."

Torres subsequently constructed working prototypes based on his theoretical designs. In 1911, at the request of French mathematician Maurice d’Ocagne, he published a description of his complete electromechanical calculating machine in the Encyclopédie Scientifique.^[155][156] In 1914 and 1920, Torres demonstrated that wheel-work mechanisms in calculating machines—such as Babbage's—could be replaced with electromechanical components. His 1914 analytical machine was a scaled-down demonstration device exhibited in Paris; it used a small memory built with electromagnets to evaluate the expression ${\displaystyle a=(p\times q)-B}$ using very small numbers. By entering a series of values for p, q, and b, the machine calculated and recorded the resulting values of ${\displaystyle a}$.^[157] The practical feasibility of this electromechanical design was confirmed when the system reached completion in his 1920 device.^[134][158]

During a conference in Paris in 1920, commemorating the centenary of the invention of Charles Xavier Thomas' mechanical arithmometer, Torres captured the attention of attendees with the demonstration of the "Arithmomètre Électromécanique" (Electromechanical Arithmometer).^[159] This machine featured an arithmetic unit linked to a typewriter—which could potentially be located remotely—enabling users to input commands and receive automatically printed results.^[134] Although the calculator was not programmable, it could perform all four arithmetic operations;^[160][161] for instance, typing instructions such as "365 × 256" followed by "=", printed "93440" and then advanced to the next line.^[162] From a user interface perspective, this machine can be regarded as a predecessor to modern computers that utilize a keyboard as an input interface.^[163] In terms of application, its design anticipated remote computing via extended electrical wires, serving as a rudimentary precursor to modern online systems that rely on communication lines. Torres had no intention of commercializing the device, viewing it instead as a vehicle to demonstrate his concepts and engineering techniques.^[164] In his accompanying paper,^[165] he also noted the necessity for automatic machines to represent continuous numerical values as finite, discrete values for processing and evaluation,^[161] an insight that directly corresponds to current digital data processing.

The electromechanical computing methods pioneered by Torres were later extended by Louis Couffignal in his 1938 doctoral thesis, Sur l'analyse mécanique. Application aux machines à calculer et aux calculs de la mécanique céleste.^[166] Referring to Torres' work, Couffignal sought to extend the possibilities of automatic calculation and advocated the use of the binary system in future electromechanical calculating machines. In 1939, he submitted a proposal for an automatic calculating machine to the French National Centre for Scientific Research (CNRS), though the outbreak of World War II brought the effort to a halt,^[167] shortly before the major advances in computing that would take place during the 1940s.^[168]

Naval engineering

In those days when the outbreak of the Great War was anticipated, Torres designed a transport ship intended to accompany fleets. On 30 July 1913, he patented the "Buque campamento" ("Camp-Vessel"),^[169] an airship carrier featuring his innovative mooring mast technology and a hold large enough to house up to two inflated units. By integrating a stable mooring system on deck, he sought to efficiently combine aeronautics with naval operations, offering his patent to Vickers Limited, although the conglomerate did not show interest in the project. Negotiations continued, and Torres reached Admiral Reginald Bacon, who, on 17 March 1914, wrote from the Coventry Ordnance Works that "the experience of the Navy has invariably been that any auxiliary craft carried on board ship are of very little real service." In 1922, the Spanish Navy commissioned the Dédalo—the first ship to operate both captive airships and seaplanes—and similar arrangements would later appear in airship support vessels such as the American USS Patoka, incorporating concepts that Torres had proposed years earlier with his 1913 "Camp-Vessel" design.^[170]

In 1916 Torres patented in Spain a new kind of ship, a multihull steel vessel which received the name of "Binave" ("Twin Ship").^[171] He applied for the patent of the Binave in the United Kingdom with the name "Improvements in Ships" in 1917.^[172] It was built by the Euskalduna company in Bilbao in 1918, with several test departures such as the successful round trip to Santoña on 28 September. The tests would be resumed in 1919, obtaining the certificate of implementation of the patent on 12 November of that year. The design introduces several structural features, including two 30 HP Hispano-Suiza marine engines, articulated joints intended to modify its configuration and counteract sea-induced torsion, two rudders located at the stern of each float, and aft-mounted propellers. The twin hulls were intended to accommodate machinery and tanks, while the structure above them provided space for cargo, passengers and crew. Based on the data acquired during these trials, a lower keel was added to each float in 1920 to improve stability, employing design principles that closely parallel modern catamarans, due to its lightweight structure, the use of the twin hulls for machinery and tanks and a hull spacing close to proportions considered optimal in contemporary multihull design which became widespread from the 1990s onward.^[173][174]

Other inventions and miscellaneous activities

Apart from the aforementioned inventions, Torres patented the "Indicadores coordinados" ("Coordinate Indicator", 1901), a guidance system for vehicles and pedestrians using markers installed on streetlights throughout an entire city, which he proposed for Madrid and Paris under the name of "Guide Torres".^[175][176] He also patented the "Dianemologo" (1907), an apparatus for copying a speech as it is delivered without the need for shorthand,^[177] the "Globos fusiformes deformables" ("Deformable Fusiform Balloons", 1914), a fusiform envelope with a variable section depending on the volume of the hydrogen contained,^[178] and the "Enclavamientos T.Q." ("Interlocks T.Q.", 1918), a railway interlock of his own design to protect the movement of trains within a certain area.^[179][180]

In the final years of his career, Torres focused on diverse innovations, patenting improvements to typewriters (1922–23)^[181] and the marginal pagination of books (1926).^[182] He then turned his attention to the field of educational disciplines, researching elements and machines to assist educators in their tasks. His most prominent educational contributions came in 1930 with the patenting of the "Puntero Proyectable" (Projectable Pointer, 1930),^[183] and the "Proyector Didáctico" (Didactic Projector, 1930).^[184] The Projectable Pointer was based on the shadow produced on a plate or screen by a moving opaque body, which allowed the presenter to move the pointer to any place on the plate (today a slide) and operate it with an articulated system. Likewise, the Didactic Projector improved the way slides were mounted on glass plates for projection.^[185][186]